NANYANG TECHNOLOGICAL UNIVERSITY School of Electrical & Electronic Engineering

DESIGN AND INNOVATION PROJECT

DESIGN OF NARROWBAND AND BROADBAND

WILKINSON POWER DIVIDER

Group Number: 07

Supervisor Name: Dr. Jeffrey Fu

Dr. Lee Ching Kwang

Student Name: Huang Guangpu

Qing Songlin

Date: 31 May, 2006

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Table of Contents

Abstract........................................................................................................................4

1 Introduction..................................................................5

2 Design Method.............................................................6

3 Calculations.................................................................8

4 Evaluation by Simulations.........................................10

4.1 Sigle-section Wilkinson power divider................10

4.2 Multi-section power divider.................................13

5 Discussion and Recommendations............................16

6 Conclusion.................................................................18

7 Reference List............................................................19

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Abstract

Wilkinson power divider is a lossless, 100% efficient, three port network with matched

outputs. It splits an input signal into two equal phase output signals. Two sorts of

Wilkinson power dividers were investigated in our project: narrowband Wilkinson in

phase 3dB power divider (11.5-12.5 GHz), and broadband Wilkinson in phase 3dB power

divider (6-18 GHz). The broadband Wilkinson power dividers were designed on the basis

of the single-section circuit with more than two sections employed. It was found that the

Wilkinson power dividers cannot perform well with theoretical values. However, this

problem could be solved by fine tuning.

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1 Introduction

Power divider/splitter is a passive microwave component used for power division or

power combining. One major type, known as Wilkinson power divider, is a lossless three

port network with one input port and two output ports, where the output ports are

simultaneously isolated and matched [4]. It could be applied to balance amplifiers, high-

power transmitters, and antenna array feed networks [1].

There are two types of Wilkinson power divider, namely equal power divider and

unequal power divider. In our investigation equal power divider, which splits an input

signal into two equal phase output signals, was designed and applied accordingly.

Moreover, single-section and multi-section Wilkinson power dividers were constructed to

operate in narrowband (11.5-12.5GHz) and broadband (6-18 GHz) regions respectively

[2].

In this report, method of schematic design, graphic design, layout design, and Gerber

design for fabrications will firstly be introduced, followed by evaluation through

simulations. Then related discussions and further recommendations will be presented and

conclusion will be drawn.

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2 Design Method

Power divider usually employs quarterwave transmission line sections at the design

center frequency, and Wilkinson power consists of two quarterwave line segmetns at the

center frequency f0 with characteristic impedance √2Z0, and a 2Z0 lumped resistor

connected between the output ports [2]. Such is the design of Wilkinson power divider

that it provides low loss, equal-split (ideally 3 dB) matching at all ports and high isolation

between output ports (figure 1) [4].

Figure 1 Wilkinson equal power divider

As shown in the figure above, there are four different sections [2].

1. Input port

2. Quarter-wave transformer

3. Isolation resistors

4. Output ports

Input and output ports are identical with impedance value Z0 [2] .

Quarter-wave transformer parts are characterized by the length of these parts, which are

equal to one fourth of the wavelength of the electromagnetic wave, which is propagating

in this three port network. This length is also related to the operation frequency g [5].

Nominal Wavelength 0 * Centre frequency f = Phase velocity V0

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Operation wavelength

The quarter-wave transformers are used in the circuit since they lead to the matched

ports. Matching of the output ports is necessary for better power transfer from input to

output, because if the output ports are matched, the reflected power from the network

when we input some amount of power is zero. This means, there is no reflection from the

outputs and all of the power is transmitted to the output ports [3].

Isolation resistor is to isolate the output ports. If there is a coupling effect between output

ports, in other words, the power comes from one output port has an effect on the other

output port, the perfect division of the power would be impossible. This isolation resistor

avoids the coupling effects of the output ports [2].

Output ports are the terminals that divided power comes out. These ports have the same

impedance value Z0 as the input port [2].

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3 Calculations

As provided, the micro strip circuit was constructed on a substrate with Er = ErNorm =

2.5 and h=0.75mm.

There are two ways to determine the width of the quarter-wave transformer. First method

is the graph method, where from the figure below (figure 2), width-height ratio could be

figured out to be 2.8, therefore w = 2.8*0.75 = 2.1mm.

Figure 2 Microstrip characteristic impedance as a function of w/h and

And the width could be also determined by calculation method using the following

equations.

For w/h < 1

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For w/h > 1

Applying the above equations to verify the value obtained through graph method:

w=2.08mm, which is very close to 2.1. Therefore, w=2.1mm.

As mentioned in the design method section, input and output impedances are of the same

impedance of the isolation resistor Z0 = 50Ω, where the quarter wave length transformer

maintain the impedance of .

Nominal Wavelength 0 * Centre frequency f = Phase velocity V0

Or mmf

v25

10^10*12

8^10*3

0

00

Operation wavelength

Then the length of quarter-wave transformer is 3.95mm.

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4 Evaluation by Simulations

4.1 Sigle-section Wilkinson power divider

Based on the calculations shown above, the first phase design of narrow-band Wilkinson

power divider was constructed on a substrate with Er=2.5 and H=0.75 mm(figure 3). The

first design made use of the existing Wilkinson power divider model in Micro-Wave

Office database by applying the calculated values.

Figure 3 Schematic representation of narrowband

Wilkinson power divider (first phase design)

However, the first phase design was not ready for fabrication; more detailed circuit

should be designed. By adding bends and junctions and carefully adjusting the values, a

second-phased design of narrowband Wilkinson power divider was constructed (figure

4).

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Figure 4 Schematic representation of single-section

Wilkinson power divider (first design)

From narrow-band power divider second phase design, the following optimied result

could be obtained (Graph5).

Figure 5 Schematic illustration of performance ofNarrow-band Wilkinson power divider design

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In the figure above, S21, S31 are the voltage ratios from the output ports to input port.

Theoretically, power ratio of equal three-port Wilkinson power divider is 0.5 since the

input signal is equally divided into two parts. Therefore, voltage ratios

and S21, S31 = 20log0.707 = -3dB [4].

From the figure above, it could be observed that an upward parabolic curve with a peak

value of -3.1559dB at the central frequency, approximately the ideal value -3dB; the

voltage gain at Frequency 11.5 GHz and 12.5 GHz are -3.2543dB and -3.2333 dB

respectively, which are within the range of +/-0.1 dB with respect to the centre frequency

gain. Applying larger scale on y-axis, voltage gain, we are able to get a flat top with -3

dB gain value in the narrow band region, 11.5~12.5 GHz. The result is of satisfaction

considering the acceptable errors and defects in the design. Moreover, curves of S21, S31

overlap together, indicating a good equal division of the input signal [6].

The layout of the narrow-band Wilkinson power divider second phase design is shown

below (figure 6). The green rectangle is the resisitor.

Figure 6 Layout of narrow-band Wilkinson power divider (left:2D right: 3D)

The dimension of the narrow-band Wilkinson power divider is 20.26 mm*14.13mm, so

the whole micro stripe circuit can be confined within a 1 inch* 1 inch substrate. The size

of the resistor is 1.3mm* 2.0mm.

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The design shown above could effectively split input power into two equal phase output

signals in narrowband region 11.5~12.5 GHz. However, its performance is poor for

broad-band frequency signals. In fact, broadband matching could be achieved through

multi-stage imposition of single stage equal power dividers.

4.2 Multi-section power dividerMulti-section power divider is approached upon the basis of narrow-band Wilkinson 3 dB

power divider (figure 7). With more isolation from the resistor in each stage, better

performance is expected from the design [3].

Figure 7 Schematic representation of broadbandWilkinson power divider

Multi-section power divider was also designed on the basis of the same substrate with

Er=2.5 and H=0.75 mm.

From broad-band power divider design, the following optimized result could be obtained

(figure 8).

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Figure 8 Schematic illustration of performance ofBroad-band Wilkinson power divider design

As mentioned previously, S21, S31 are the voltage ratios from the output ports to input port

and S21, S31 = 20log0.707 = -3dB.

From the figure above, we can observe an oscillating curve with a central peak of

-3.109dB. And the values of other peaks except the last one are also close to -3.109dB.

The value at the centre frequency 12GHz is -3.16dB, approximately the ideal value -3dB;

the voltage gain at Frequency 6GHz and 18GHz are -3.359dB and -4.839dB respectively.

Applying larger scale on y-axis, voltage gain, we are able to get a flat top with -3 dB gain

value in the region from 6GHz to 17GHz. However, the ratio declines sharply after

17GHz due to elementary limitation of the micro-stripe circuit.

The layout of the broad-band Wilkinson power divider is shown below (figure9).

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Figure 9 Layout of broad-band Wilkinson power divider (left:2D right:3D)

Figure 11 Layout of broad-band Wilkinson power divider-3D

The dimension of the broad-band Wilkinson power divider is 25 mm*14 mm, so the

whole micro stripe circuit can be confined within a 1 inch* 1 inch substrate. The size of

the resistor is 1.3mm* 2.0mm.

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5 Discussion and Recommendations

1 Parameter ajustment:

It was found that both the narrowband and broadband Wilkinson power dividers cannot

perform well with the theoretical values after adding the junctions and bends. For

simplicity, only narrowband Wilkinson power divider is taken out for illustration.

Although our first phase design (figure 3) which made use of the model in MWO

database could effectively divide the input signal into two equal output signals, the

second design which includes bends and junctions could not perform well. Therefore, it is

necessary to tune the values.

For single-section Wilkinson power divider, the values to be adjusted are shown below

(figure 10).

Figure 10 Notation of parameters in single-section Wilkinson power divider

As observed, the center of curves for S21, S31 shifted to the left of 12GHz after adding the

bends and junctions. To increase the center frequency, lengths of the transformers should

be decreased. Moreover, in order to keep curves of S21 and S31 overlapping, symmetric

lengths were adjusted to a same value (eg. L2 and L3, L4 and L5).

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It was found that values of L1, L10 and L11 did not affect the output much. And so was

R1, where the reason might be that no current flows through the resistor in equal

Wilkinson power divider. Other lengths (from L2 to L9) were carefully adjusted to get

the optimized result (figure 3). Generally, except L4 and L5 were increased a bit, other

lengths were all decreased (chart 1).

Name L1 L2 L3 L4 L5 L6Value(mm) 5.9 3.5 3.5 4.3 4.3 2.05

Name L7 L8 L9 L10 L11 R1Value(mm) 0.4 0.4 2.05 5.9 5.9 100 Ω

Chart 1 Parameters of narrowband Wilkinson power divider

2 Error analysis: Refer to figure 5 and 8; For narrow band power divider design, the

value at the centre frequency 12GHz is -3.1599dB, approximately the ideal value -3dB,

(3.1599-3)/3=5.33% ; the voltage gain at Frequency 11.5 GHz and 12.5 GHz are -

3.2543dB and -3.2333 dB respectively, (3.2543-3)/3=8.48% (3.2333-3)/3=7.78%

%. Therefore, the graph is within the desired range, and it would be approximately

ideal. For broadband power divider design, at the centre frequency 12GHz is -3.16dB; the

voltage gain at Frequency 6GHz and 18GHz are -3.359dB and -4.839dB respectively.

(3.16-3)/3=5.33% (3.359-3)/3=11.97% (4.839-3)/3=61.3%

Design defect: By choosing different micro-stripe elements, e.g. MBEND90X Mitered

90deg (EM Based) and MCURVE function differently as they work most effectively in

different frequency range. In actual design, MCURVE adds to the transformer

wavelength extra length, which affects the frequency response of the divider, while

MBEDN90X does not contribute any extra length due to geometrical property.

Recommendation: The performance of 3-dB Wilkinson Power Divider could be

effectively improved by fine-tuning and layout adjustment. Tuning process takes place

among the symmetrical micro-stripe length in the schematic circuit e.g. L6 and L9

(Figure10) should maintain the same value in order to keep output voltage ratio in phase.

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6 Conclusion

Wilkinson equal power divider is a passive microwave component which could

effectively divide input power into two identical output parts without any power loss,

power gain ratio -3 Db. It basically contains four parts: one input port, quarter-wave

transformers, isolation resistor and two output ports. In this report, 3 dB Wilkinson Power

Divider design, single-stage and multi-stage, were approached based on related theories

and calculation. It was found that the isolated resistor absorbs no power, and the quarter-

wave transformers length affects the output ports power gain and phase difference. Single

section Wilkinson power divider splits input power with frequency range 11.5-12.5 GHz,

and the narrowband design could be extended to broadband design applying three single

stages together. Possible errors and defects of both single-stage and multi-stage

Wilkinson power dividers were investigated to optimize the result in the design.

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7 Reference List

[1] Brady Dana, “The design, fabrication and measurement of microstrip filter and

coupler circuits,” High Frequency Electronics., Jul 2002.

[2] I. KASA, Microwave Integrated Circuits, Elsevier, 1991.

[3] Mitsuyoshi Kishihara et al., “A Design of Multi-Stage, Multi-Way Microstrip

Power Dividers with Broadband Properties” IEEE MTT-S Digest, 2004.

[4] Howe, “Stripline Circuit Design”, Artech House, 1974.

[5] Helszajn, “Microwave Planar Passive Circuits and Filters”, Wilery, 1994.

[6] Internet Source:

http://www.microwaves101.com/encyclopedia/Wilkinson_splitters.cfm

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